Leveraged fund drag

A fund that resets to L times an index every day grows, in the typical case, at about r + L·(μ − r) − fee − L²·σ²/2. Put in your guesses and see whether the leverage pays.

3x trails the index in the typical case.

• Typical growth: 3x -0.7% a year vs index 7.6% (volatility drag on 3x: 21.8%).
• Average growth: 3x 21.1% a year. The average keeps rising with leverage; the typical outcome doesn't.
• Break-even: the index must beat cash by more than 10.2% a year (your inputs: 6.0%).
• Best leverage for typical growth with these inputs: 1.24x.
• After 10 years: median 0.93× for 3x vs 2.13× for the index; mean 8.21×.
• Chance 3x ends ahead of the index after 10 years: 28%. Chance it ends below where it started: 51%.

Typical growth by leverage

Orange: typical yearly growth at each leverage with your inputs. Dashed: the index. Past the peak, more leverage means less growth.

From a terminal

curl 'https://lev.wickkit.cc/?mu=10&vol=22&r=4&L=3'
curl 'https://lev.wickkit.cc/api?mu=8&vol=16&L=2'   # JSON (rates come back as decimals)

Assumes steady volatility and lognormal daily moves. Real volatility spikes when prices fall, which hurts leverage more than this says. Swap costs run a little above the cash rate. μ is the input nobody knows. Not advice. The derivation and a simulation are in The Break-Even Line for 3x.

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